It is known from the state of the art, in the case of comparable methods, to project a so-called Gray code onto the object together with the stripe pattern which makes it possible to identify individual pairs of lines of the stripe pattern in images of the stripe pattern recorded on the object and thus to identify image points associated with specific object points, which enables triangulation for detection of a three-dimensional contour of the object. A disadvantage of methods of this type according to the state of the art resides in the fact that, because of the projection of relatively comprehensive information onto the object, a large number of recordings is required. This militates in particular against use of such methods in hand-held devices. The object therefore underlying the present invention is to propose a device and a corresponding method for the contactless detection of a three-dimensional contour, which avoid the mentioned disadvantages and, in particular with respect to an intraoral or extraoral detection of tooth surfaces or surfaces of tooth models or dentures, allow manual handling at least of one measuring head which is used.